17,988 research outputs found
Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives
We consider the problem of finding commuting self-adjoint extensions of the
partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain
C_c^\infty(\Omega) where the self-adjointness is defined relative to
L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is
Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E.
Segal and B. Fuglede, and is difficult in general. In this paper, we provide a
representation-theoretic answer in the special case when \Omega=I\times\Omega_2
and I is an open interval. We then apply the results to the case when \Omega is
a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that
{e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal
basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km,
02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt,
61.44.B
Predicting Lotto Numbers
We investigate the "law of small numbers" using a unique panel data set on lotto gambling. Because we can track individual players over time, we can measure how they react to outcomes of recent lotto drawings. We can therefore test whether they behave as if they believe they can predict lotto numbers based on recent drawings. While most players pick the same set of number week after week without regards of numbers drawn or anything else, we find that those who do change, act on average in the way predicted by the law of small numbers as formalized in recent behavioral theory. In particular, on average they move away from numbers that are on streak, i.e. have been drawn several weeks in a row, consistent with the "hot hand fallacy".gambler's fallacy;hot hand fallacy;representativeness;law of small numbers
The Sloan-Lens ACS Survey II: stellar populations and internal structure of early-type lens galaxies
We derive Fundamental Plane parameters of 15 early-type lens galaxies
identified by the Sloan Lens ACS (SLACS) Survey. The size of the sample allows
us to investigate for the first time the distribution of lens galaxies in the
FP space. After correcting for evolution, we find that lens galaxies occupy a
subset of the local FP. The edge-on projection (approximately M vs M/L) is
indistinguishable from that of normal early-type galaxies. However -- within
the fundamental plane -- the lens galaxies appear to concentrate at the edge of
the region populated by normal early-type galaxies. We show that this is a
result of our selection procedure (approximately velocity dispersion
sigma>240km/s). We conclude that SLACS lenses are a fair sample of high
velocity dispersion early-type galaxies. By comparing the central stellar
velocity dispersion that of the best fit lens model, we find
== =1.01+-0.02 with 0.065 rms scatter. We conclude that
within the Einstein radii the SLACS lenses are very well approximated by
isothermal ellipsoids, requiring a fine tuning of the stellar and dark matter
distribution (bulge-halo ``conspiracy''). Interpreting the offset from the
local FP in terms of evolution of the stellar mass-to-light ratio, we find for
the SLACS lenses d log M/L_B/dz=-0.69+-0.08 (rms 0.11) consistent with the rate
found for field early-type galaxies and with a scenario where most of the stars
were formed at high redshift (>2) with secondary episodes of star formation
providing less than ~10% of the stellar mass below z=1. We discuss star
formation history and structural homogeneity in the context of formation
mechanisms such as collisionless (``dry'') mergers. [Abridged]Comment: 2006, ApJ, 604, 622; 13 pages, 7 figures, 2 tables. Replaced Table 2,
since the previous version was incorrectly sorted. Updated references. No
changes in plots or content. More info available at SLACS website
www.slacs.or
Observations of nitrogen isotope fractionation in deeply embedded protostars
(Abridged) The terrestrial planets, comets, and meteorites are significantly
enriched in 15N compared to the Sun and Jupiter. While the solar and jovian
nitrogen isotope ratio is believed to represent the composition of the
protosolar nebula, a still unidentified process has caused 15N-enrichment in
the solids. Several mechanisms have been proposed to explain the variations,
including chemical fractionation. However, observational results that constrain
the fractionation models are scarce. While there is evidence of 15N-enrichment
in prestellar cores, it is unclear how the signature evolves into the
protostellar phases. Our aim is to measure the 14N/15N ratio around three
nearby, embedded low-to-intermediate-mass protostars. Isotopologues of HCN and
HNC were used to probe the 14N/15N ratio. A selection of H13CN, HC15N, HN13C,
and H15NC transitions was observed with the APEX telescope. The 14N/15N ratios
were derived from the integrated intensities assuming a standard 12C/13C ratio.
The assumption of optically thin emission was verified using radiative transfer
modeling and hyperfine structure fitting. Two sources, IRAS 16293A and R CrA
IRS7B, show 15N-enrichment by a factor of around 1.5-2.5 in both HCN and HNC
with respect to the solar composition. Solar composition cannot be excluded for
the third source, OMC-3 MMS6. Furthermore, there are indications of a trend
toward increasing 14N/15N ratios with increasing outer envelope temperature.
The enhanced 15N abundances in HCN and HNC found in two Class~0 sources
(14N/15N of 160-290) and the tentative trend toward a temperature-dependent
14N/15N ratio are consistent with the chemical fractionation scenario, but
14N/15N ratios from additional tracers are indispensable for testing the
models. Spatially resolved observations are needed to distinguish between
chemical fractionation and isotope-selective photochemistry.Comment: Accepted for publication in Astronomy and Astrophysics. 16 pages, 13
figure
Inhibition of MDR1 does not sensitize primitive chronic myeloid leukemia CD34<sup>+</sup> cells to imatinib
<p><b>Objective:</b> To investigate the interaction of imatinib mesylate (IM) with the clinically relevant adenosine triphosphate-binding cassette efflux transporter MDR1 (ABCB1) in cells from patients with chronic myeloid leukemia (CML) and to explore whether inhibition of this transporter would improve IM's efficacy in the elimination of CML CD34<sup>+</sup> cells by increasing cell-associated drug accumulation.</p>
<p><b>Materials and Methods:</b> Cells from newly diagnosed chronic-phase CML patients were harvested by leukapheresis and enriched to >95% CD34<sup>+</sup>. Expression of the transporter gene MDR1 was performed by quantitative reverse transcription polymerase chain reaction. Interaction of IM with MDR1 was analyzed by substrate (rhodamine 123) displacement assay. Cell-associated levels of IM in CML CD34<sup>+</sup> cells were measured by high-pressure liquid chromatography. Intracellular phospho-CrkL levels, apoptosis in total CML CD34<sup>+</sup> cells and high-resolution tracking of cell division were assayed by flow cytometry.</p>
<p><b>Results:</b> Measurements of cell-associated IM uptake showed significantly lower drug levels in CD34<sup>+</sup> cells, particularly the CD38<sup>-</sup> subpopulation, as compared to IM-sensitive K562 cells. MDR1 was expressed at low level and dye efflux studies demonstrated very little MDR1 activity in CML CD34<sup>+</sup> cells. Furthermore, combination treatment of primitive CML cells with IM and the MDR1 inhibitor PSC833 did not result in elevated cell-associated IM levels. Although we observed slightly enhanced cytostasis with IM when combined with PSC833, this was independent of BCR-ABL inhibition because no associated decrease in phospho-CrkL was observed.</p>
<p><b>Conclusions:</b> Our findings demonstrate that inhibition of MDR1 neither enhances the effect of IM against BCR-ABL activity, nor significantly potentiates IM's efficiency in eliminating primitive CML cells.</p>
Dependence of the Superconducting Transition Temperature of MgB2 on Pressure to 20 GPa
The dependence of Tc on nearly hydrostatic pressure has been measured for an
isotopically pure (11B) MgB2 sample in a helium-loaded diamond-anvil-cell to
nearly 20 GPa. Tc decreases monotonically with pressure from 39.1 K at ambient
pressure to 20.9 K at 19.2 GPa. The initial dependence is the same as that
obtained earlier (dTc/dP = -1.11(2) K/GPa) on the same sample in a He-gas
apparatus to 0.7 GPa. The observed pressure dependence Tc(P) to 20 GPa can be
readily described in terms of simple lattice stiffening within standard
phonon-mediated BCS superconductivity.Comment: 9 pages, 3 figure
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